Question: Solve for $x$ : $4\sqrt{x} - 8 = 7\sqrt{x} + 9$
Explanation: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 8) - 4\sqrt{x} = (7\sqrt{x} + 9) - 4\sqrt{x}$ $-8 = 3\sqrt{x} + 9$ Subtract $9$ from both sides: $-8 - 9 = (3\sqrt{x} + 9) - 9$ $-17 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-17}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{17}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.